GATE2018 ME-1: GA-10

Question

Consider the following three statements:

1. Some roses are red.
2. All red flowers fade quickly.
3. Some roses fade quickly.

Which of the following statements can be logically inferred from the above statements?

• A. If (i) is true and (ii) is false, then (iii) is false.
• B. If (i) is true and (ii) is false, then (iii) is true.
• C. If (i)  and (ii) are true, then (iii) is true.
• D. If (i)  and (ii) are false, then (iii) is false.

Comments

C.

some roses are red and all red flowers fade quickly => some roses fade quickly

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please correct me where i am wrong .

Answer 1

Some roses are red
and
All red flowers fade quickly
implies
Some roses fade quickly.
So, if (i) and (ii) are TRUE, (iii) must be TRUE.

Correct Answer: C.

Answer 2

$\color{Blue}{\text{Blue}}$ color shaded area represents, Some roses fade quickly.

$(I\: \wedge \: II) \implies III$

$(T \wedge T) \implies T$

So, the correct answer is $(C).$

Comments

fir to last option bhi ssahe ho jayaga asa ma @lakshman patel RJIT

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no see loption B example for it

Answer 3

option c is correct